Long Division Steps Calculator

Long Division Steps Calculator

Use this calculator to perform long division and see a detailed, step-by-step breakdown of the process. Understand how the quotient and remainder are derived for any two positive integers.

Understanding Long Division

Long division is a fundamental arithmetic method for dividing large numbers, breaking down the division process into a series of simpler steps. It's particularly useful when the dividend (the number being divided) is large and the divisor (the number dividing it) is a multi-digit number, making mental calculation difficult.

Key Terms:

• Dividend: The number being divided.
• Divisor: The number by which the dividend is divided.
• Quotient: The result of the division, indicating how many times the divisor fits into the dividend.
• Remainder: The amount left over after the division, when the dividend is not perfectly divisible by the divisor.

How Long Division Works (The Steps):

The process of long division involves a repetitive cycle of dividing, multiplying, subtracting, and bringing down digits. Here's a simplified overview:

1. Divide: Take the first digit (or first few digits) of the dividend that form a number greater than or equal to the divisor. Divide this partial dividend by the divisor.
2. Multiply: Multiply the quotient digit you just found by the divisor.
3. Subtract: Subtract the product from the partial dividend.
4. Bring Down: Bring down the next digit from the original dividend to form a new partial dividend.
5. Repeat: Continue these steps until all digits of the dividend have been brought down and processed. The final remainder is the number left after the last subtraction.

Using the Long Division Steps Calculator

Our Long Division Steps Calculator simplifies this process by showing you each step in detail. Simply enter your dividend and divisor into the respective fields and click "Calculate Steps." The calculator will then output the final quotient and remainder, along with a clear, numbered list of every operation performed.

Example: Dividing 1234 by 56

Let's use the example numbers pre-filled in the calculator: Dividend = 1234, Divisor = 56.

When you input these values and click "Calculate Steps," the calculator will perform the following operations:

1. Initially, we look at '1'. Since 1 is less than 56, we consider '12'. Still less than 56. So we take '123'.
2. Step 1: Bring down 1. Current partial dividend: 1. Since 1 < 56, the quotient digit is 0. Current remainder: 1.
3. Step 2: Bring down 2. Current partial dividend: 12. Since 12 < 56, the quotient digit is 0. Current remainder: 12.
4. Step 3: Bring down 3. Current partial dividend: 123. Divide 123 by 56. Quotient digit: 2. Multiply 2 × 56 = 112. Subtract 123 – 112 = 11. Current remainder: 11.
5. Step 4: Bring down 4. Current partial dividend: 114. Divide 114 by 56. Quotient digit: 2. Multiply 2 × 56 = 112. Subtract 114 – 112 = 2. Current remainder: 2.

The final result will show a Quotient of 22 and a Remainder of 2. This means 1234 divided by 56 is 22 with 2 left over (1234 = 56 × 22 + 2).

This tool is excellent for students learning long division, for checking homework, or for anyone who needs to quickly understand the mechanics of a division problem.

Quotient:

Remainder:

Long Division Steps:

"; for (var i = 0; i < dividendStr.length; i++) { currentPartialDividend = currentPartialDividend * 10 + parseInt(dividendStr[i]); stepsHtml += "
1. "; stepsHtml += "Bring down " + dividendStr[i] + ". Current partial dividend: " + currentPartialDividend + "."; if (currentPartialDividend < divisor) { quotient += "0"; stepsHtml += "Since " + currentPartialDividend + " < " + divisor + ", the quotient digit is 0. Current remainder: " + currentPartialDividend + "."; } else { var qDigit = Math.floor(currentPartialDividend / divisor); var product = qDigit * divisor; var remainder = currentPartialDividend – product; quotient += qDigit; stepsHtml += "Divide " + currentPartialDividend + " by " + divisor + ". Quotient digit: " + qDigit + "."; stepsHtml += "Multiply " + qDigit + " × " + divisor + " = " + product + "."; stepsHtml += "Subtract " + currentPartialDividend + " – " + product + " = " + remainder + "."; stepsHtml += "Current remainder: " + remainder + "."; currentPartialDividend = remainder; } stepsHtml += "
"; } stepsHtml += "

Quotient:

Remainder: